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<meta property="og:description" content="欠拟合与过拟合 欠拟合：模型不能有效拟合数据集对现有数据集学习的不够彻底 过拟合：模型对训练集拟合的太好，而缺失了泛化力 欠拟合的解决方法： 增加输" />
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                        <h1 class="single-title flipInX">TensorFlow2.1入门学习笔记(8)——欠拟合与过拟合(正则化)</h1><div class="post-meta summary-post-meta"><span class="post-category meta-item">
                                <a href="/categories/tf2.1%E5%AD%A6%E4%B9%A0%E7%AC%94%E8%AE%B0/"><span class="svg-icon icon-folder"></span>TF2.1学习笔记</a>
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                                <span class="svg-icon icon-clock"></span><time class="timeago" datetime="2020-05-21">2020-05-21</time>
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                                <span class="svg-icon icon-pencil"></span>约 1405 字
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        <li><a href="#欠拟合与过拟合">欠拟合与过拟合</a>
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              <ul>
                <li>
                  <ul>
                    <li><a href="#正则化缓解过拟合">正则化缓解过拟合</a></li>
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                    </div><h3 id="欠拟合与过拟合" class="headerLink"><a href="#%e6%ac%a0%e6%8b%9f%e5%90%88%e4%b8%8e%e8%bf%87%e6%8b%9f%e5%90%88" class="header-mark"></a>欠拟合与过拟合</h3><ul>
<li>欠拟合：模型不能有效拟合数据集对现有数据集学习的不够彻底</li>
<li>过拟合：模型对训练集拟合的太好，而缺失了泛化力</li>
</ul>
<!-- more -->
<p>




<figure class="render-image"><a target="_blank" href="https://img-blog.csdnimg.cn/20200519223104858.png" title=" " >
        <img loading="lazy" decoding="async"
             class="render-image"
             src="https://img-blog.csdnimg.cn/20200519223104858.png"
            alt=" "
        />
    </a><figcaption class="image-caption"> </figcaption>
</figure></p>
<ul>
<li>欠拟合的解决方法：
增加输入特征项
增加网络参数
减少正则化参数</li>
<li>过拟合的解决方法：
数据清洗
增大训练集
采用正则化
增大正则化参数</li>
</ul>
<h6 id="正则化缓解过拟合" class="headerLink"><a href="#%e6%ad%a3%e5%88%99%e5%8c%96%e7%bc%93%e8%a7%a3%e8%bf%87%e6%8b%9f%e5%90%88" class="header-mark"></a>正则化缓解过拟合</h6><p>正则化在损失函数中引入模型复杂度指标，利用给W加权值，弱化了训练
数据的噪声（一般不正则化b）</p>
<p>




<figure class="render-image"><a target="_blank" href="https://img-blog.csdnimg.cn/20200519223935333.png" title=" " >
        <img loading="lazy" decoding="async"
             class="render-image"
             src="https://img-blog.csdnimg.cn/20200519223935333.png"
            alt=" "
        />
    </a><figcaption class="image-caption"> </figcaption>
</figure></p>
<ul>
<li><strong>常见的正则化：</strong>
$loss_{l_1}(w)=\sum_i |w_i|$
$loss_{l_1}(w)=\sum_i |w_i ^2|$</li>
<li><strong>正则化的选择：</strong>
L1正则化大概率会使很多参数变为零，因此该方法可通过稀疏参数，即减少参数的数量，降低复杂度。
L2正则化会使参数很接近零但不为零，因此该方法可通过减小参数值的大小降低复杂度。</li>
<li>例如：给出一个<a href="https://download.csdn.net/download/moonoa/12443841" target="_blank" rel="noopener noreffer">dot.csv数据集</a>，判断y_是1的可能性大还是0的可能性大。</li>
<li>思路：可以将x1、x2分别作为横纵坐标，y_为1的点标为红色，为0的点标为蓝色，在坐标系中展示出来，通过神经网络离合出分界线模型。</li>
<li>采用l2正则化的源码：</li>
</ul>
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<pre class="chroma"><code class="language-python" data-lang="python"><span class="c1"># 导入所需模块</span>
<span class="kn">import</span> <span class="nn">tensorflow</span> <span class="kn">as</span> <span class="nn">tf</span>
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>
<span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pandas</span> <span class="kn">as</span> <span class="nn">pd</span>

<span class="c1"># 读入数据/标签 生成x_train y_train</span>
<span class="n">df</span> <span class="o">=</span> <span class="n">pd</span><span class="o">.</span><span class="n">read_csv</span><span class="p">(</span><span class="s1">&#39;dot.csv&#39;</span><span class="p">)</span>
<span class="n">x_data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">df</span><span class="p">[[</span><span class="s1">&#39;x1&#39;</span><span class="p">,</span> <span class="s1">&#39;x2&#39;</span><span class="p">]])</span>
<span class="n">y_data</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">df</span><span class="p">[</span><span class="s1">&#39;y_c&#39;</span><span class="p">])</span>

<span class="n">x_train</span> <span class="o">=</span> <span class="n">x_data</span>
<span class="n">y_train</span> <span class="o">=</span> <span class="n">y_data</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>

<span class="n">Y_c</span> <span class="o">=</span> <span class="p">[[</span><span class="s1">&#39;red&#39;</span> <span class="k">if</span> <span class="n">y</span> <span class="k">else</span> <span class="s1">&#39;blue&#39;</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">y_train</span><span class="p">]</span>

<span class="c1"># 转换x的数据类型，否则后面矩阵相乘时会因数据类型问题报错</span>
<span class="n">x_train</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">cast</span><span class="p">(</span><span class="n">x_train</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
<span class="n">y_train</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">cast</span><span class="p">(</span><span class="n">y_train</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>

<span class="c1"># from_tensor_slices函数切分传入的张量的第一个维度，生成相应的数据集，使输入特征和标签值一一对应</span>
<span class="n">train_db</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">data</span><span class="o">.</span><span class="n">Dataset</span><span class="o">.</span><span class="n">from_tensor_slices</span><span class="p">((</span><span class="n">x_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">))</span><span class="o">.</span><span class="n">batch</span><span class="p">(</span><span class="mi">32</span><span class="p">)</span>

<span class="c1"># 生成神经网络的参数，输入层为4个神经元，隐藏层为32个神经元，2层隐藏层，输出层为3个神经元</span>
<span class="c1"># 用tf.Variable()保证参数可训练</span>
<span class="n">w1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span> <span class="mi">11</span><span class="p">]),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
<span class="n">b1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="p">[</span><span class="mi">11</span><span class="p">]))</span>

<span class="n">w2</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">([</span><span class="mi">11</span><span class="p">,</span> <span class="mi">1</span><span class="p">]),</span> <span class="n">dtype</span><span class="o">=</span><span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
<span class="n">b2</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">Variable</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">constant</span><span class="p">(</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">shape</span><span class="o">=</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>

<span class="n">lr</span> <span class="o">=</span> <span class="mf">0.005</span>  <span class="c1"># 学习率为</span>
<span class="n">epoch</span> <span class="o">=</span> <span class="mi">800</span>  <span class="c1"># 循环轮数</span>

<span class="c1"># 训练部分</span>
<span class="k">for</span> <span class="n">epoch</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">epoch</span><span class="p">):</span>
    <span class="k">for</span> <span class="n">step</span><span class="p">,</span> <span class="p">(</span><span class="n">x_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">train_db</span><span class="p">):</span>
        <span class="k">with</span> <span class="n">tf</span><span class="o">.</span><span class="n">GradientTape</span><span class="p">()</span> <span class="k">as</span> <span class="n">tape</span><span class="p">:</span>  <span class="c1"># 记录梯度信息</span>

            <span class="n">h1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">x_train</span><span class="p">,</span> <span class="n">w1</span><span class="p">)</span> <span class="o">+</span> <span class="n">b1</span>  <span class="c1"># 记录神经网络乘加运算</span>
            <span class="n">h1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="n">h1</span><span class="p">)</span>
            <span class="n">y</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">h1</span><span class="p">,</span> <span class="n">w2</span><span class="p">)</span> <span class="o">+</span> <span class="n">b2</span>

            <span class="c1"># 采用均方误差损失函数mse = mean(sum(y-out)^2)</span>
            <span class="n">loss_mse</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">reduce_mean</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">square</span><span class="p">(</span><span class="n">y_train</span> <span class="o">-</span> <span class="n">y</span><span class="p">))</span>
            <span class="c1"># 添加l2正则化</span>
            <span class="n">loss_regularization</span> <span class="o">=</span> <span class="p">[]</span>
            <span class="c1"># tf.nn.l2_loss(w)=sum(w ** 2) / 2</span>
            <span class="n">loss_regularization</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">l2_loss</span><span class="p">(</span><span class="n">w1</span><span class="p">))</span>		<span class="c1">#对w1使用l2正则化处理</span>
            <span class="n">loss_regularization</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">l2_loss</span><span class="p">(</span><span class="n">w2</span><span class="p">))</span>
            <span class="c1"># 求和</span>
            <span class="c1"># 例：x=tf.constant(([1,1,1],[1,1,1]))</span>
            <span class="c1">#   tf.reduce_sum(x)</span>
            <span class="c1"># &gt;&gt;&gt;6</span>
            <span class="n">loss_regularization</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">reduce_sum</span><span class="p">(</span><span class="n">loss_regularization</span><span class="p">)</span>
            <span class="n">loss</span> <span class="o">=</span> <span class="n">loss_mse</span> <span class="o">+</span> <span class="mf">0.03</span> <span class="o">*</span> <span class="n">loss_regularization</span>  <span class="c1"># REGULARIZER = 0.03</span>

        <span class="c1"># 计算loss对各个参数的梯度</span>
        <span class="n">variables</span> <span class="o">=</span> <span class="p">[</span><span class="n">w1</span><span class="p">,</span> <span class="n">b1</span><span class="p">,</span> <span class="n">w2</span><span class="p">,</span> <span class="n">b2</span><span class="p">]</span>
        <span class="n">grads</span> <span class="o">=</span> <span class="n">tape</span><span class="o">.</span><span class="n">gradient</span><span class="p">(</span><span class="n">loss</span><span class="p">,</span> <span class="n">variables</span><span class="p">)</span>

        <span class="c1"># 实现梯度更新</span>
        <span class="c1"># w1 = w1 - lr * w1_grad</span>
        <span class="n">w1</span><span class="o">.</span><span class="n">assign_sub</span><span class="p">(</span><span class="n">lr</span> <span class="o">*</span> <span class="n">grads</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
        <span class="n">b1</span><span class="o">.</span><span class="n">assign_sub</span><span class="p">(</span><span class="n">lr</span> <span class="o">*</span> <span class="n">grads</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
        <span class="n">w2</span><span class="o">.</span><span class="n">assign_sub</span><span class="p">(</span><span class="n">lr</span> <span class="o">*</span> <span class="n">grads</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
        <span class="n">b2</span><span class="o">.</span><span class="n">assign_sub</span><span class="p">(</span><span class="n">lr</span> <span class="o">*</span> <span class="n">grads</span><span class="p">[</span><span class="mi">3</span><span class="p">])</span>

    <span class="c1"># 每200个epoch，打印loss信息</span>
    <span class="k">if</span> <span class="n">epoch</span> <span class="o">%</span> <span class="mi">20</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
        <span class="k">print</span><span class="p">(</span><span class="s1">&#39;epoch:&#39;</span><span class="p">,</span> <span class="n">epoch</span><span class="p">,</span> <span class="s1">&#39;loss:&#39;</span><span class="p">,</span> <span class="nb">float</span><span class="p">(</span><span class="n">loss</span><span class="p">))</span>

<span class="c1"># 预测部分</span>
<span class="k">print</span><span class="p">(</span><span class="s2">&#34;*******predict*******&#34;</span><span class="p">)</span>
<span class="c1"># xx在-3到3之间以步长为0.01，yy在-3到3之间以步长0.01,生成间隔数值点</span>
<span class="n">xx</span><span class="p">,</span> <span class="n">yy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mgrid</span><span class="p">[</span><span class="o">-</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span><span class="p">:</span><span class="o">.</span><span class="mi">1</span><span class="p">,</span> <span class="o">-</span><span class="mi">3</span><span class="p">:</span><span class="mi">3</span><span class="p">:</span><span class="o">.</span><span class="mi">1</span><span class="p">]</span>
<span class="c1"># 将xx, yy拉直，并合并配对为二维张量，生成二维坐标点</span>
<span class="n">grid</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">c_</span><span class="p">[</span><span class="n">xx</span><span class="o">.</span><span class="n">ravel</span><span class="p">(),</span> <span class="n">yy</span><span class="o">.</span><span class="n">ravel</span><span class="p">()]</span>
<span class="n">grid</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">cast</span><span class="p">(</span><span class="n">grid</span><span class="p">,</span> <span class="n">tf</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>
<span class="c1"># 将网格坐标点喂入神经网络，进行预测，probs为输出</span>
<span class="n">probs</span> <span class="o">=</span> <span class="p">[]</span>
<span class="k">for</span> <span class="n">x_predict</span> <span class="ow">in</span> <span class="n">grid</span><span class="p">:</span>
    <span class="c1"># 使用训练好的参数进行预测</span>
    <span class="n">h1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">([</span><span class="n">x_predict</span><span class="p">],</span> <span class="n">w1</span><span class="p">)</span> <span class="o">+</span> <span class="n">b1</span>
    <span class="n">h1</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">nn</span><span class="o">.</span><span class="n">relu</span><span class="p">(</span><span class="n">h1</span><span class="p">)</span>
    <span class="n">y</span> <span class="o">=</span> <span class="n">tf</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">h1</span><span class="p">,</span> <span class="n">w2</span><span class="p">)</span> <span class="o">+</span> <span class="n">b2</span>  <span class="c1"># y为预测结果</span>
    <span class="n">probs</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>

<span class="c1"># 取第0列给x1，取第1列给x2</span>
<span class="n">x1</span> <span class="o">=</span> <span class="n">x_data</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span>
<span class="n">x2</span> <span class="o">=</span> <span class="n">x_data</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span>
<span class="c1"># probs的shape调整成xx的样子</span>
<span class="n">probs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">probs</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">xx</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">squeeze</span><span class="p">(</span><span class="n">Y_c</span><span class="p">))</span>
<span class="c1"># 把坐标xx yy和对应的值probs放入contour函数，给probs值为0.5的所有点上色  plt.show()后 显示的是红蓝点的分界线</span>
<span class="n">plt</span><span class="o">.</span><span class="n">contour</span><span class="p">(</span><span class="n">xx</span><span class="p">,</span> <span class="n">yy</span><span class="p">,</span> <span class="n">probs</span><span class="p">,</span> <span class="n">levels</span><span class="o">=</span><span class="p">[</span><span class="o">.</span><span class="mi">5</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>

<span class="c1"># 读入红蓝点，画出分割线，包含正则化</span>
</code></pre></td></tr></table>
</div>
</div><ul>
<li>学习结果</li>
</ul>
<p>




<figure class="render-image"><a target="_blank" href="https://img-blog.csdnimg.cn/20200521180804105.png" title=" " >
        <img loading="lazy" decoding="async"
             class="render-image"
             src="https://img-blog.csdnimg.cn/20200521180804105.png"
            alt=" "
        />
    </a><figcaption class="image-caption"> </figcaption>
</figure></p>
<p>相比于不使用正则化，分界线更平滑有效缓解了过拟合，泛化性更好</p>
<p>




<figure class="render-image"><a target="_blank" href="https://img-blog.csdnimg.cn/20200521180823296.png" title=" " >
        <img loading="lazy" decoding="async"
             class="render-image"
             src="https://img-blog.csdnimg.cn/20200521180823296.png"
            alt=" "
        />
    </a><figcaption class="image-caption"> </figcaption>
</figure></p>
<p>主要学习的资料，西安科技大学：<a href="https://www.icourse163.org/learn/XUST-1206363802#/learn/announce" target="_blank" rel="noopener noreffer">神经网络与深度学习——TensorFlow2.0实战</a>，北京大学：<a href="https://www.icourse163.org/learn/PKU-1002536002#/learn/announce" target="_blank" rel="noopener noreffer">人工智能实践Tensorflow笔记</a></p>
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